Modified Callen decoupling in the Green's-function theory of Heisenberg antiferromagnets

The modified Callen decoupling (MCD) is extended to Heisenberg antiferromagnets with exchange between more than nearest neighbors. The results are illustrated by application to type-I order in the three cubic lattices. It is shown that type-I order in simple cubic and body-centered-cubic lattices is especially simple---and therefore especially stable---due to several accidental symmetries. The more general case is typified by type-I order in a face-centered-cubic lattice, which shows an instability at intermediate temperatures for all values of the exchange constants when S=1/2. The MCD results are compared to the Pad\'e-approximant estimates of the N\'eel temperatures and are shown to explain the anomalous behavior found for spin {}.